Statistics PYQs - Last 10 Years

JEE Main / Mathematics / Algebra / 129 recent questions

MathematicsAlgebra2017-2026

All Statistics PYQs Last 5 Years Create chapter test

Practice 129 JEE Main Mathematics questions from Statistics. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.

129

PYQs on Page

Mathematics / Algebra

2017-2026

Year Range

Based on indexed question metadata

74

Last 5 Years

2022-2026

129

Last 10 Years

2017-2026

Recent Year Trend

2021

2022

2023

2024

2025

2026

202122 max PYQs/year2026

Question Types

129PYQs

MCQ70.5%

INTEGER29.5%

Difficulty Mix

#1 Medium100

#2 Easy25

#3 Hard4

74 in last 5 years129 in last 10 years

Last 10 Years Statistics Questions

Showing 29 of 129 filtered questions.

Consider the data on x taking the values 0, 2, 4,
8,....., 2n with frequencies nC0
,
nC1
,
nC2
,....,
nCn
respectively. If the mean of this data is \({{728} \over {{2^n}}}\), then n is equal to _________ .

INTEGER+4 / -02020

The mean and variance of 7 observations are 8 and 16, respectively. If five observations are 2, 4, 10, 12, 14, then the absolute difference of the remaining two observations is :

If the mean and the standard deviation of the
data 3, 5, 7, a, b are 5 and 2 respectively, then
a and b are the roots of the equation :

The mean and variance of 8 observations are 10 and 13.5, respectively. If 6 of these observations
are 5, 7, 10, 12, 14, 15, then the absolute difference of the remaining two observations is :

If the variance of the following frequency
distribution :
Class : 10–20 20–30 30–40

Frequency : 2 x 2
is 50, then x is equal to____

INTEGER+4 / -02020

For the frequency distribution :
Variate (x) :      x1   x2   x3
.... x15
Frequency (f) : f1
   f2
  f3
...... f15
where 0 < x1
< x2
< x3
< ... < x15 = 10 and
\(\sum\limits_{i = 1}^{15} {{f_i}}\) > 0, the standard deviation cannot be ...

Let xi
(1 \(\le\) i \(\le\) 10) be ten observations of a
random variable X. If \(\sum\limits_{i = 1}^{10} {\left( {{x_i} - p} \right)} = 3\) and \(\sum\limits_{i = 1}^{10} {{{\left( {{x_i} - p} \right)}^2}} = 9\) where 0 \(\ne\) p ...

Let X = {x
\(\in\) N : 1
\(\le\) x
\(\le\) 17} and
Y = {ax + b: x
\(\in\) X and a, b \(\in\) R, a > 0}. If mean
and variance of elements of Y are 17 and 216
respectively then a + b is equal to :

If the variance of the terms in an increasing A.P., b1
, b2
, b3
,....,b11 is 90, then the common
difference of this A.P. is_______.

INTEGER+4 / -02020

5 students of a class have an average height 150 cm and variance 18 cm2. A new student, whose height is 156 cm, joined them. The variance (in cm2) of the height of these six students is :

A data consists of n observations : x1, x2, . . . . . . ., xn.
If \(\sum\limits_{i = 1}^n {{{\left( {{x_i} + 1} \right)}^2}} = 9n\) and
\(\sum\limits_{i = 1}^n {{{\left( {{x_i} - 1} \right)}^2}} = 5n,\)
then the standard devi...

If the standard deviation of the numbers
–1, 0, 1, k is \(\sqrt 5\) where k > 0, then k is equal to

The mean and the median of the following ten
numbers in increasing order 10, 22, 26, 29, 34, x,
42, 67, 70, y are 42 and 35 respectively, then \({y \over x}\) is equal to

The mean and variance of seven observations are
8 and 16, respectively. If 5 of the observations are
2, 4, 10, 12, 14, then the product of the remaining
two observations is :

A student scores the following marks in five tests
:
45, 54, 41, 57, 43.
His score is not known for the
sixth test. If the mean score is 48 in the six tests,
then the standard deviation of the marks in six tests
is

If the sum of the deviations of 50 observations from 30 is 50, then the mean of these observations is :

The mean and the variance of five observations are 4 and 5.20, respectively. If three of the observations are
3, 4 and 4 ; then the absolute value of the difference of the other two observations, is :

If the data x1, x2,......., x10 is such that the mean of first four of these is 11, the mean of the remaining six is
16 and the sum of squares of all of these is 2,000 ; then the standard deviation of this data is :

The outcome of each of 30 items was observed; 10 items gave an outcome \({1 \over 2}\) – d each, 10 items gave outcome \({1 \over 2}\) each and the remaining 10 items gave outcome \({1 \over 2}\)+ d each. If the variance of this outcome dat...

The mean of five observations is 5 and their variance is 9.20. If three of the given five observations are 1, 3 and 8, then a ratio of other two observations is -

If mean and standard deviation of 5 observations x1, x2, x3, x4, x5 are 10 and 3, respectively, then the variance of 6 observations x1, x2, ….., x5 and –50 is equal to

If for some x \(\in\) R, the frequency distribution of the marks obtained by 20 students in a test is :

.tg {border-collapse:collapse;border-spacing:0;}
.tg td{font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:s...

If both the mean and the standard deviation of 50 observations x1, x2,..., x50 are equal to 16, then the mean of (x1 – 4)2
, (x2 – 4)2
,....., (x50 – 4)2
is :

The mean and the standard deviation(s.d.) of five observations are9 and 0, respectively. If one of the observations is changed such that the mean of the new set of five observations becomes 10, then their s.d. is :

The mean of set of 30 observations is 75. If each observation is multiplied by a non-zero number \(\lambda\) and then each of them is decreased by 25, their mean remains the same. Then \(\lambda\) is equal to :

If the mean of the data : 7, 8, 9, 7, 8, 7, \(\lambda\), 8 is 8, then the variance of this data is :

If \(\sum\limits_{i = 1}^9 {\left( {{x_i} - 5} \right)} = 9\) and
\(\sum\limits_{i = 1}^9 {{{\left( {{x_i} - 5} \right)}^2}} = 45\), then the standard deviation of the 9 items
\({x_1},{x_2},.......,{x_9}\) is

The sum of 100 observations and the sum of their squares are 400 and 2475,
respectively. Later on, three observations, 3, 4 and 5, were found to be incorrect. If
the incorrect observations are omitted, then the variance of the remaining obs...

The mean age of 25 teachers in a school is 40 years. A teacher retires at the age of 60 years and a new teacher is appointed in his place. If now the mean age of the teachers in this school is 39 years, then the age (in years) of the newly...